1. The renormalization preserves the diffeomorphism invariance
(general covariance) of the model of QG in four
spacetime dimensions (i.e., in \(n=4\) ), if the initial classical
theory possesses this symmetry. This means, one can remove
the divergences in all loop orders by adding covariant counterterms.
This statement applies literally only to the divergences that take
place in the framework of the background field method, which is
especially designed to avoid non-covariant counterterms. Let us
stress that the background field method is not necessary for the
gauge-invariant renormalization in QG. However,
using the non-covariant parametrization of the metric, such as
(REF ), one has to go through a relatively complicated
procedure or additional renormalization transformations, as
described in [1]}. The final output is always the same
in the sense of the same essential covariant counterterms.
For this reason, in what follows we shall assume (REF )
when evaluating the power counting in different models of QG.
However, we shall switch to the more general parametrization with
the general background metric (REF ) when making the
practical calculations.
